Abstract
In this paper we show that several algorithmic problems for abelian black-box groups and solvable black-box groups are low for PP. In particular, we prove that Membership Testing, Group Intersection, Order Verification, and Group Isomorphism for abelian groups are in SPP, and Group Factorization, Coset Intersection, and Double Coset Membership for abelian groups are in LWPP. Similarly, we show that Membership Testing, Order Verification, and Group Isomorphism for solvable groups are in ZPPSPP. We also show that Group Intersection, Group Factorization, Coset Intersection, and Double Coset Membership for solvable groups are low for PP.
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© 1996 Springer-Verlag Berlin Heidelberg
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Arvind, V., Vinodchandran, N.V. (1996). Solvable black-box group problems are low for PP. In: Puech, C., Reischuk, R. (eds) STACS 96. STACS 1996. Lecture Notes in Computer Science, vol 1046. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60922-9_9
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DOI: https://doi.org/10.1007/3-540-60922-9_9
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